I have attached a word document that contains my question. In the attached document R( ) is the row space, N( ) is the null space, and C( ) is the column space.
If you were to let A be a 6 x 14 matrix where the dimension of the row space is 3 (dim(R(A) = 3), what would the dimension of the null space of matrix A (dim(N(A)) be and what would the dimension of the null space of A^T (dim(N(A^T)) be?
Also, if you let B be a 6 x 6 invertible matrix, what would dim(N(BA)^orthogonal complement) and dim(C(A^TB^T)^orthogonal complement) be? (C( ) is the column space)